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1、绝对运动
若动点是相对于静参考系的运动，则称为绝对运动;
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3、牵连运动
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2、相对运动
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3、牵连运动
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1、绝对运动
若动点是相对于静参考系的运动，则称为绝对运动;
2、相对运动
若动点是相对于动参考系的运动，则称为相对运动;
3、牵连运动
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                                <h2>
                                    2.4 科氏加速度 比力 比力方程
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                                    2023-09-22, 758 words, 3 min read
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                                        <h2 id="一-运动形式的描述">一、运动形式的描述</h2>
<h4 id="1-绝对运动">1、绝对运动</h4>
<p>若<strong>动点</strong>是相对于<strong>静参考系</strong>的运动，则称为绝对运动;</p>
<h4 id="2-相对运动">2、相对运动</h4>
<p>若<strong>动点</strong>是相对于<strong>动参考系</strong>的运动，则称为相对运动;</p>
<h4 id="3-牵连运动">3、牵连运动</h4>
<p>若是<strong>动参考系</strong>相对于<strong>静参考系</strong>的运动则称为牵连运动。</p>
<p>绝对运动是相对运动和牵连运动的合成运动</p>
<h2 id="二-科氏加速度">二、科氏加速度</h2>
<h4 id="1-定义">1、定义</h4>
<p>当动点相对某一动参考系作相对运动，该动参考系又在做牵连运动，则该动点具有科氏加速度。</p>
<h4 id="2-公式">2、公式</h4>
<p>设牵连角速度为 <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>w</mi></mrow><annotation encoding="application/x-tex">w</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.02691em;">w</span></span></span></span>，动点的相对运动速度 <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>v</mi><mi>r</mi></msub></mrow><annotation encoding="application/x-tex">v_r</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em;">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> ，</p>
<p>科氏加速度公式   <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>a</mi><mi>c</mi></msub><mo>=</mo><mn>2</mn><mi>w</mi><mo>×</mo><msub><mi>v</mi><mi>r</mi></msub></mrow><annotation encoding="application/x-tex">a_c=2w×v_r</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord">2</span><span class="mord mathdefault" style="margin-right:0.02691em;">w</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em;">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></p>
<h4 id="3-产生原因">3、产生原因</h4>
<ol>
<li>当动点的牵连运动为转动时，牵连运动会使相对速度的方向不断发生改变。</li>
<li>而相对运动又使牵连速度的大小不断发生改变。</li>
<li>这两种原因都造成了同一方向上附加的速度变化率，该附加的速度变化率即为哥氏加速度。</li>
</ol>
<h2 id="三-绝对加速度">三、绝对加速度</h2>
<h4 id="1-定义-2">1、定义</h4>
<p>当动点的牵连运动为转动时，动点的绝对加速度等于相对加速度、牵连加速度、科氏加速度的矢量和</p>
<h4 id="2-公式-2">2、公式</h4>
<p><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="bold">a</mi><mo>=</mo><msub><mi mathvariant="bold">a</mi><mi>r</mi></msub><mo>+</mo><msub><mi mathvariant="bold">a</mi><mi>e</mi></msub><mo>+</mo><msub><mi mathvariant="bold">a</mi><mi>c</mi></msub></mrow><annotation encoding="application/x-tex">\mathbf{a}=\mathbf{a}_r+\mathbf{a}_e+\mathbf{a}_c</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.44444em;vertical-align:0em;"></span><span class="mord"><span class="mord mathbf">a</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.73333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord"><span class="mord mathbf">a</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em;">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.73333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord"><span class="mord mathbf">a</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">e</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.59444em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord"><span class="mord mathbf">a</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></p>
<h2 id="四-科氏转动定理">四、科氏转动定理</h2>
<h4 id="1-定义-3">1、定义</h4>
<p>在固定坐标系中，一个向量对时间的变化率（绝对变化率）等于同一向量在动坐标系中对时间的变化率(相对变化率)与动坐标系对固定坐标系的旋转角速度向量和该向量本身的向量积之和</p>
<h4 id="2-公式-3">2、公式</h4>
<img src="http://cos.pansis.site/202309221614325.png/abc123" alt="image-20230922161455266" style="zoom:33%;" />
<h4 id="3-运载体绝对加速度表达式">3、运载体绝对加速度表达式</h4>
<p>从i系推导至e系</p>
<figure data-type="image" tabindex="1"><img src="http://cos.pansis.site/202309221620668.png/abc123" alt="image-20230922162046559" loading="lazy"></figure>
<h4 id="4-推导">4、推导</h4>
<img src="http://cos.pansis.site/202309221624167.png/abc123" alt="image-20230922162417056" style="zoom:33%;" />
<img src="http://cos.pansis.site/202309221624026.png/abc123" alt="image-20230922162425960" style="zoom:33%;" />
<h2 id="五-比力">五、比力</h2>
<h4 id="1-定义-4">1、定义</h4>
<p>作用在单位质量上的惯性力与引力的合力（量纲依旧为加速的的量纲）</p>
<h4 id="2-公式-4">2、公式</h4>
<p>比力=弹力/质量</p>
<figure data-type="image" tabindex="2"><img src="http://cos.pansis.site/202309221645301.png/abc123" alt="image-20230922164547224" loading="lazy"></figure>
<h4 id="3-比力的作用">3、比力的作用</h4>
<ul>
<li>比力的大小与弹簧变形量成正比</li>
<li>加速度计输出电压的大小与弹簧变 形量成正比</li>
<li>所以加速度计实际感测的量并非是运载体的加速度，而是比力</li>
<li>加速度计又称为比力敏感器</li>
</ul>
<h4 id="4-例题">4、例题</h4>
<figure data-type="image" tabindex="3"><img src="http://cos.pansis.site/202309221647188.png/abc123" alt="image-20230922164717086" loading="lazy"></figure>
<figure data-type="image" tabindex="4"><img src="http://cos.pansis.site/202309221647598.png/abc123" alt="image-20230922164723533" loading="lazy"></figure>
<figure data-type="image" tabindex="5"><img src="http://cos.pansis.site/202309221655790.png/abc123" alt="image-20230922165539702" loading="lazy"></figure>
<h2 id="六-比力方程">六、比力方程</h2>
<h4 id="1-方程">1、方程</h4>
<img src="http://cos.pansis.site/202309221656824.png/abc123" alt="image-20230922165642782" style="zoom: 35%;" />
<img src="http://cos.pansis.site/202311091418502.png/abc123" alt="image-20231109141809368" style="zoom:43%;" />
<h4 id="2-物理意义">2、物理意义</h4>
<ul>
<li><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>f</mi></mrow><annotation encoding="application/x-tex">f</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord mathdefault" style="margin-right:0.10764em;">f</span></span></span></span> 为加速度计输出的比力信息</li>
</ul>
<p><strong>比力方程表明了加速度计测得的比力与运载体现象对地球的加速度之间的关系</strong></p>
<figure data-type="image" tabindex="6"><img src="http://cos.pansis.site/202309221659070.png/abc123" alt="image-20230922165914995" loading="lazy"></figure>
<h4 id="3-推导">3、推导</h4>
<figure data-type="image" tabindex="7"><img src="http://cos.pansis.site/202309221704789.png/abc123" alt="image-20230922170431699" loading="lazy"></figure>
<figure data-type="image" tabindex="8"><img src="http://cos.pansis.site/202309221706503.png/abc123" alt="image-20230922170658434" loading="lazy"></figure>
<figure data-type="image" tabindex="9"><img src="http://cos.pansis.site/202309221707911.png/abc123" alt="image-20230922170722831" loading="lazy"></figure>
<h4 id="4-补偿功能">4、补偿功能</h4>
<p><strong>导航计算中需要的是</strong>运载体相对地球的加速度 <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mover accent="true"><mi>v</mi><mo>˙</mo></mover></mrow><annotation encoding="application/x-tex">\dot{v}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.66786em;vertical-align:0em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.66786em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em;">v</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.11111000000000001em;">˙</span></span></span></span></span></span></span></span></span>，因此<strong>必须从加速度计测得的比力中补偿有害加速度 <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>a</mi><mi>B</mi></msub></mrow><annotation encoding="application/x-tex">a_B</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.05017em;">B</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>的影响。</strong></p>
<img src="http://cos.pansis.site/202309221712402.png/abc123" alt="image-20230922171212348" style="zoom:33%;" />
<h4 id="5">5、</h4>
<p>根据安装加速度计的测量坐标系的不同，可以 得到运载体相对地球运动时加速度计所敏感的不同比力表达式</p>
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